Random attractor of stochastic Brusselator system with multiplicative noise

Junyi  Tu; Yuncheng You

doi:10.3934/dcds.2016.36.2757

Article Contents

2016, Volume 36, Issue 5: 2757-2779. Doi: 10.3934/dcds.2016.36.2757

This issue Previous Article From gradient theory of phase transition to a generalized minimal interface problem with a contact energy Next Article Local well-posedness and blow-up phenomena for a generalized Camassa-Holm equation with peakon solutions

Random attractor of stochastic Brusselator system with multiplicative noise

Junyi Tu^1, and
Yuncheng You^1,

1.
Department of Mathematics and Statistics, University of South Florida, Tampa, FL 33620-5700

Received: November 30, 2014

Revised: July 31, 2015

Published: May 2017

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Abstract

Asymptotic dynamics of stochastic Brusselator system with multiplicative noise is investigated in this work. The existence of random attractor is proved via the exponential transformation of Ornstein-Uhlenbeck process and some challenging estimates. The proof of pullback asymptotic compactness here is more rigorous through the bootstrap pullback estimations than a non-dynamical substitution of Brownian motion by its backward translation. It is also shown that the random attractor has the attracting regularity to be an $(L^2\times L^2,H^1\times H^1)$ random attractor.

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Mathematics Subject Classification: 37L30, 35B40, 35B41, 35K55, 80A32, 92B05.

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